{
  "id": "math/0703403",
  "version": "v1",
  "published": "2007-03-14T03:19:22.000Z",
  "updated": "2007-03-14T03:19:22.000Z",
  "title": "Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball",
  "authors": [
    "G. Kyriazis",
    "P. Petrushev",
    "Yuan Xu"
  ],
  "comment": "30 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Weighted Triebel-Lizorkin and Besov spaces on the unit ball $B^d$ in $\\Rd$ with weights $\\W(x)= (1-|x|^2)^{\\mu-1/2}$, $\\mu \\ge 0$, are introduced and explored. A decomposition scheme is developed in terms of almost exponentially localized polynomial elements (needlets) $\\{\\phi_\\xi\\}$, $\\{\\psi_\\xi\\}$ and it is shown that the membership of a distribution to the weighted Triebel-Lizorkin or Besov spaces can be determined by the size of the needlet coefficients $\\{\\ip{f,\\phi_\\xi}\\}$ in appropriate sequence spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-14T03:19:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A25",
      "42B35",
      "42C15"
    ],
    "keywords": [
      "besov spaces",
      "weighted triebel-lizorkin",
      "appropriate sequence spaces",
      "unit ball",
      "decomposition scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3403K"
    }
  }
}